McDermott scored 21 of his 33 points in the second half to lead the 23rd-ranked Bluejays in an 82-72 victory over Tulsa on Saturday.
But it was Chatman who kept Creighton in the game in the first half. He made six of his first seven shots, including all three of his 3-pointers, and had 15 of his career-high 19 points in the first 20 minutes.
"I shot the first one and everything after that felt good," the junior point guard said. "My teammates did a good job of finding me. Compliments to my teammates."
McDermott recorded his 16th career 30-point game. He also became the first Creighton player since Cyril Baptiste in 1969-70 to open a season with four straight 20-point games.
The Bluejays (4-0), playing as a Top 25 team for the first time this season, opened the second half on a 13-4 run to increase its 42-41 halftime lead to 55-45. McDermott had eight points during the spurt, closing the surge with two straight 3-pointers.
"We definitely weren't our sharpest today," Creighton coach Greg McDermott said, "but fortunately we got a great performance out of Austin, Doug was outstanding, and it was enough to carry us."
Chatman was 4 for 5 from long range and had nine assists.
"We knew he was a capable shooter," Tulsa coach Danny Manning said. "Did I expect him to go 4 of 5 from 3? No. You've got to make your game plan and take something away and give something up. He walked into a couple shots and knocked them down."
Doug McDermott played a strong all-around game, grabbing 15 rebounds. He also made three 3-pointers, 12 of 15 free throws and had a couple of steals.
The two-time first-team All-American always has been a capable rebounder, but it's become more of an emphasis since the graduation of Gregory Echenique.
"I tended to leak out a little because I knew Gregory would get every board around the rim," Doug McDermott said, "so I was a little more flexible and could get out in transition and run a little more. This year I think I'm definitely going to have to step up and rebound a lot more. I've really focused on that here the last week or so at practice."
Creighton held an eight- to 12-point lead for most of the second half until Tulsa made a late run. Rashad Smith banked in a shot off Rashad Ray's fast-break pass, got fouled by Devin Brooks and made the free throw to make it a seven-point game. Smith scored again after a Brooks turnover to make it 73-68 with 3:51 left.
The Hurricane had a chance to make it a one-possession game with 2 minutes left, but Swilling was way off with a 3, and McDermott hit a long shot on the other end to restore the Bluejays' eight-point advantage.
Creighton led by one at halftime, thanks to a Chatman 3-pointer with five seconds left.
"The one at half was on me," Manning said, "because I said we wanted to play softer, and he launched one deep and it went in. He's the engine that makes this team go, as far as pushing the team in transition and distributing the ball."
Chatman's fourth 3-pointer came early in the second-half run that broke open the game. McDermott followed with two shots from beyond the arc, the second one ripping the net as he fell backward.
Creighton has won 45 of 46 regular-season November home games since 1990. Tulsa hasn't beaten a ranked opponent since Dayton in the 2003 NCAA tournament.
The Bluejays have won four straight in the series against their one-time Missouri Valley Conference rival. Now they're off until they play Arizona State on Thanksgiving night at the Wooden Legacy tournament in Fullerton, Calif.
"We're going to see a legitimate top-20 team on Thursday in Arizona State," Greg McDermott said. "We will have to play better than we played today on the defensive end of the floor."
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.